We study the dynamics of type I strings on Melvin backgrounds, with a single
or multiple twisted two-planes. We construct two inequivalent types of
orientifold models that correspond to (non-compact) irrational versions of
Scherk-Schwarz type breaking of supersymmetry. In the first class of vacua,
D-branes and O-planes are no longer localized in space-time but are smeared
along the compact Melvin coordinate with a characteristic profile. On the other
hand, the second class of orientifolds involves O-planes and D-branes that are
both rotated by an angle proportional to the twist. In case of ``multiple
Melvin spaces'', some amount of supersymmetry is recovered if the planes are
twisted appropriately and part of the original O-planes are transmuted into new
ones. The corresponding boundary and crosscap states are determined.Comment: 34 pages, LaTe